Finite Group Databasebeta

← #28390976

Subgroups — #28390976

Order 14464.

344 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813610C211yesmaximal, characteristic
2#20299075C211yesmaximal, characteristic, complemented
3#20298604C211yesmaximal, characteristic
4#20298602C211yesmaximal, characteristic
5C2×#16813540C211yesmaximal, characteristic, complemented
6#20298358C211yesmaximal, characteristic, complemented
7#339×C113C211yesmaximal, characteristic, complemented
8C22×Dic226C2211yescharacteristic
9C22×D452C2211yescharacteristic
10C2×#14268631C2211yescharacteristic
11#16813610—22no—
12#16813610C414yescomplemented
13C4×Dic226—22no—
14#16813587—22no—
15#16813581C2211yescharacteristic
16#16813578—22no—
17C2×#14268624—22no—
18#16813544—22no—
19#16813542—22no—
20#16813540—22no—
21C2×M16×C113C2211yescharacteristic
22#117×C113C2211yescharacteristic
23C2×C42×C113C2211yescharacteristic
24C23×D113—21no—
25C2×Dic226—21no—
26C2×Dic226—21no—
27C2×Dic226—21no—
28C2×Dic226—21no—
29C2×Dic226C2×C412yes—
30C2×Dic226D412yes—
31C2×D452—21no—
32C2×D452—21no—
33C2×D452—21no—
34C2×D452—21no—
35C2×D452—21no—
36C2×D452C2×C412yes—
37C22×Dic113D412yes—
38#14268631—21no—
39#14268631—21no—
40C2×#11744751—21no—
41C4⋊Dic113D412yes—
42#14268626—24no—
43C22⋊Dic113—21no—
44#14268624—28no—
45C4×Dic113—24no—
46C4×Dic113—21no—
47C22×C4×C113—21no—
48C22×C4×C113C2311yescharacteristic
49M16×C113—21no—
50M16×C113—21no—
51C2×C8×C113—21no—
52C4⋊C4×C113D412yes—
53C22⋊C4×C113—21no—
54C42×C113—21no—
55C42×C113—21no—
56C42×C113C2×C412yes—
57C23×C113C2×D411yescharacteristic
58C22×D113—22no—
59C22×D113—44no—
60C22×D113—41no—
61C22×D113—41no—
62C2×C4×C113—22no—
63C2×C4×C113—22no—
64C2×C4×C113—42no—
65C2×C4×C113C22×C411yescharacteristic
66C2×C4×C113C2×D411yescharacteristic
67C2×C4×C113C2×D411yescharacteristic
68C2×C4×C113C2×D411yescharacteristic
69C2×C4×C113#4111yescharacteristic
70C2×C4×C113#4111yescharacteristic
71C2×Dic113—22no—
72C2×Dic113—22no—
73C2×Dic113—22no—
74C2×Dic113C22⋊C414yes—
75D452—22no—
76D452—22no—
77D452—41no—
78D452—41no—
79Dic226—22no—
80Dic226—22no—
81Dic226—22no—
82Dic226—22no—
83C8×C113—41no—
84#11744751—41no—
85C22×C113—22no—
86C22×C113C2×C22⋊C411yescharacteristic
87C22×C113#12011yescharacteristic
88C22×C113#12311yescharacteristic
89C2×D113—44no—
90C2×D113—42no—
91C2×D113—82no—
92C2×D113—82no—
93C4×C113—42no—
94C4×C113—42no—
95C4×C113C4×D411yescharacteristic
96C4×C113C4×D411yescharacteristic
97C4×C113#12111yescharacteristic
98C4×C113#12111yescharacteristic
99Dic113—24no—
100Dic113—42no—
101C2×C113—21no—
102C2×C113—21no—
103C2×C113#38611yescharacteristic
104C2×C113#45412yes—
105D113—82no—
106#1888—1131nomaximal, Sylow
107C113#188811yescharacteristic, complemented, Sylow
108C2×#124—1131no—
109#519—1131no—
110#418—1131no—
111#418—1131no—
112C2×#101—1131no—
113#339—1131no—
114#339D11311yescharacteristic, complemented
115C22×Q8—1131no—
116C22×D4—1131no—
117C2×M16—1131no—
118C2×M16C2×D11311yescharacteristic
119#124—1134no—
120#124—2262no—
121C4×Q8—2262no—
122C4×Q8—2262no—
123#117—1131no—
124#117—2262no—
125#117C2×D11311yescharacteristic
126C2×C22⋊C4—2262no—
127C2×C42C2×D11311yescharacteristic
128#102—2262no—
129#102—2262no—
130#101—2262no—
131C24—2261no—
132C2×Q8—1132no—
133C2×Q8—1132no—
134C2×Q8—2261no—
135C2×Q8—2261no—
136C2×Q8—2261no—
137C2×Q8—2261no—
138C2×D4—1132no—
139C2×D4—2261no—
140C2×D4—2261no—
141C2×D4—2261no—
142C2×D4—2261no—
143C2×D4—2261no—
144C22×C4—21no—
145C22×C4—1132no—
146C22×C4C22×D11311yescharacteristic
147M16—21no—
148M16—21no—
149M16—2261no—
150M16—2261no—
151C2×C8—21no—
152C2×C8—2261no—
153C4⋊C4—1132no—
154C4⋊C4—2264no—
155C4⋊C4D45212yes—
156C22⋊C4—21no—
157C22⋊C4—2268no—
158C22⋊C4—2261no—
159C42—21no—
160C42—21no—
161C42—2264no—
162C42—2261no—
163C42C4×D11312yes—
164C23—4524no—
165C23—4521no—
166C23—4521no—
167C23—2262no—
168C23D4×D11311yescharacteristic
169Q8—2262no—
170Q8—2262no—
171Q8—2262no—
172Q8—2262no—
173D4—4521no—
174D4—4521no—
175D4—2262no—
176D4—2262no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—1134no—
181C2×C4—2262no—
182C2×C4—2262no—
183C2×C4—2262no—
184C2×C4C2×C4×D11311yescharacteristic
185C2×C4D4×D11311yescharacteristic
186C2×C4D4×D11311yescharacteristic
187C2×C4C2×D45211yescharacteristic
188C2×C4#1426864711yescharacteristic
189C2×C4#1426864811yescharacteristic
190C8—41no—
191C8—4521no—
192C22—22no—
193C22—9042no—
194C22—9042no—
195C22—4524no—
196C22—4522no—
197C22C22⋊C4×D11311yescharacteristic
198C22#1681359211yescharacteristic
199C22#1681360711yescharacteristic
200C4—42no—
201C4—42no—
202C4—4522no—
203C4—2264no—
204C4#1681358411yescharacteristic
205C4C4×D45211yescharacteristic
206C4#1681359511yescharacteristic
207C4#1681359711yescharacteristic
208C2—21no—
209C2—21no—
210C2—9042no—
211C2#2029847611yescharacteristic
212C2#2029877212yes—
subgroupG/H
centerC22#16813592
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
Fitting#339×C113C2
socleC22×C113#120
prime radicalC22×D452C22
cosocleC22×C4×C113C23
hypercenter#339D113
hypocenterC113#1888
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #20299075C2semidirect
5. C2×#16813540C2semidirect
6. #20298358C2semidirect
7. #339×C113C2semidirect
12. #16813610C4semidirect
107. C113#1888semidirect
114. #339D113semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168136102
#202990752
#202986042
#202986022
C2×#168135402
#202983582
#339×C1132
#1888113